This paper presents a general formal semantic scheme for the interpretation of quantum mechanics, in terms of which van Fraassen's Copenhagen and anti-Copenhagen variants of the modal interpretation are examined. The general character of the modal interpretation is motivated in a discussion of classical statistical mechanics, the distinction being made between statistical states and micro-states. The notion of a quasi-classical (micro) state is introduced in a discussion of the theorem of Gleason and Kochen and Specker. It is shown that, according to the anti-Copenhagen variant, the class of micro-states coincides with a special class of quasi-classical states. The paper concludes with two general criticisms of the anti-Copenhagen variant.